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Prépublications
Some relations between the spectra of simple and non-backtracking random walks
(2017)
Quantum Ergodicity on Graphs : from Spectral to Spatial Delocalization
(avec Mostafa Sabri),
(2017)
Publications
Delocalization of Schrödinger eigenfunctions
Proceedings ICM (2018)
Poisson kernel expansions for Schrödinger operators on trees
(avec Mostafa Sabri),
accepté à J. Spectral Theory (2017)
Recent results of quantum ergodicity on graphs and further investigation
(avec Mostafa Sabri),
accepté à Ann. Faculté des Sciences Toulouse (2017)
Quantum ergodicity on regular graphs
Comm. Math. Phys. 353 (2017), no. 2, 633-690
Quantum ergodicity for the Anderson model on regular graphs
(avec Mostafa Sabri),
J. Math. Phys. 58 (2017), no. 9
Topologie des hypersurfaces nodales de fonctions gaussiennes
Séminaire Bourbaki Vol. 2015/2016,
Astérisque 390
(2017), Exp. No. 1116, 369-408
Wigner measures and observability for the Schrödinger equation on the disk
[pdf]
(avec Matthieu Léautaud et Fabricio
Macià),
Invent. Math. 206 (2016), no. 2, 485-599
Delocalization of quasimodes on the disk
[pdf]
(avec Matthieu Léautaud et Fabricio
Macià),
C. R. Math. Acad. Sci. Paris. 354 (2016), no. 3, 257-263
Quantum ergodicity on large regular graphs
[pdf]
(avec Etienne Le Masson ),
Duke Math. J. 164 (2015), no. 4, 723-765
Quantum ergodicity and beyond (with a gallery of pictures)
[pdf] (avec Arnd Bäcker),
IAMP News Bulletin, April 2013, 10-28.
Semiclassical Completely Integrable Systems : Long-Time Dynamics And Observability Via Two-Microlocal Wigner Measures
[pdf]
(avec Clotilde Fermanian Kammerer et Fabricio
Macià),
Amer. J. Math. 137 (2015), no. 3, 577-638.
Sharp polynomial decay rates for the damped wave equation on the torus
(avec Matthieu Léautaud et avec un appendice de
Stéphane Nonnenmacher),
Anal. PDE.7 (2014), no. 1, 159-214.
The dynamics of the Schrödinger flow from the point of view of
semiclassical measures
(avec Fabricio
Macià),
article de survol, Spectral geometry, 93-116, Proc. Sympos. Pure Math., 84, AMS, 2012.
Semiclassical measures for the Schrödinger equation on the
torus
(avec Fabricio
Macià),
J. Eur. Math. Soc. 16 (2014), no. 6, 1253-1288.
A Haar component for quantum limits on locally symmetric spaces
[pdf]
(avec Lior Silberman),
Israel J. Math. 195 (2013), no. 1, 393-447
Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces [pdf] (avec Steve Zelditch),
Math. Annalen 353 (2012), no. 4, 1103-1156.
Dispersion and controllability for the Schrödinger equation on
negatively curved manifolds [pdf] (avec Gabriel Rivière),
Anal. PDE 5 (2012), no. 2, 313-338.
Exponential decay for products of Fourier integral
operators,
Methods Appl. Anal. 18 (2011), no. 2, 165-181.
A hyperbolic dispersion estimate, with applications to the linear Schrödinger equation,
Proc. ICM. Vol. III (2010).
Spectral deviations for the damped wave equation[pdf],
Geom. Funct. Anal. 20 (2010), no. 3, 59-626.
On the existence of closed geodesics,
The scientific legacy of Poincaré, 143-160, Hist. Math. 36,
Amer. Math. Soc., Providence, RI, 2010.
Vibrations chaotiques et grosses balafres (avec
Stéphane Nonnenmacher),
Gaz. Math 119 16-32 (2009).
Chaotic vibrations and strong scars (avec
Stéphane Nonnenmacher),
Eur. Math. Soc. Newsl. 74 19-24 (2009), version
anglaise remaniée du précédent.
Entropy of eigenfunctions [pdf], (avec Herbert Koch et
Stéphane Nonnenmacher),
New trends in Mathematical Physics, Proceedings of ICMP 2006,
1-22 (2009), Springer.
Half-delocalization of eigenfunctions for the Laplacian on an
Anosov manifold [pdf],
(avec
Stéphane Nonnenmacher),
Festival Colin de Verdière, Ann. Inst. Fourier 57 no. 7, 2465-2523 (2007).
Patterson-Sullivan distributions and quantum ergodicity [pdf],
(avec Steve Zelditch),
Ann. IHP. 8 no. 2, 361-426 (2007). AHP Distinguished paper.
Entropy and the localization of eigenfunctions [pdf],
Ann. Math. (2) 168 no. 2, 435-475 (2008).
Entropy and the localization of eigenfunctions [pdf],
(version non-publiée, avec la phase stationnaire en grande dimension).
Entropy of semiclassical measures of the Walsh-quantized baker's
map, [pdf],
(avec
Stéphane Nonnenmacher)
,
Ann. IHP. 8 no. 1, 37-74 (2007).
Physical solutions of the Hamilton-Jacobi equation [pdf],
(avec
Renato Iturriaga, Pablo Padilla et Hector Sanchez-Morgado),
Disc. Cont. Dyn. Syst. Ser. B 5 no. 3, 513-528 (2005).
On the zero-temperature or vanishing viscosity limit
for certain Markov processes arising from Lagrangian dynamics
[pdf],
J. Eur. Math. Soc. (JEMS) 6 no. 2, 207-276 (2004).
Counting geodesics which are optimal in homology
[pdf],
Ergodic Theory Dyn. Syst., 23 no. 2, 353-388 (2003).
Precise counting results for closed orbits of Anosov flows [pdf],
Ann. Sci. E.N.S. (4) 33 no. 1, 33-56 (2000).
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Mémoires
Entropie et localisation des fonctions propres,
[pdf],
Habilitation à diriger les recherches, ENS-Lyon, 2006.
Notes de cours
Eigenfunctions of the laplacian on negatively curved manifold :
a semiclassical approach,
[pdf],
Homogeneous flows, Moduli Spaces and Arithmetic, 389-438, Clay Math. Proc. 10, AMS, 2010.
Le théorème d'ergodicité quantique
Journées XUPS 2014
Vidéos
Cours filmé pour l'école CIMPA Théorie spectrale des graphes et des variétés , Kairouan, Tunisie, Novembre 2016